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feat: add stats/strided/smeanlipw
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‎lib/node_modules/@stdlib/stats/strided/smeanlipw/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2020 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# smeanlipw
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> Calculate the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.
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<section class="intro">
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The [arithmetic mean][arithmetic-mean] is defined as
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<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->
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```math
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\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
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```
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<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@39c6ac0ef47c7ee94007922f3602eb7e69a658c0/lib/node_modules/@stdlib/stats/strided/smeanlipw/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
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<br>
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</div> -->
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var smeanlipw = require( '@stdlib/stats/strided/smeanlipw' );
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```
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#### smeanlipw( N, x, strideX )
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Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
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var v = smeanlipw( x.length, x, 1 );
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// returns ~0.3333
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```
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The function has the following parameters:
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- **N**: number of indexed elements.
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- **x**: input [`Float32Array`][@stdlib/array/float32].
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- **strideX**: stride length for `x`.
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The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the [arithmetic mean][arithmetic-mean] of every other element in `x`,
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
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var v = smeanlipw( 4, x, 2 );
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// returns 1.25
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var v = smeanlipw( 4, x1, 2 );
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// returns 1.25
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```
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#### smeanlipw.ndarray( N, x, strideX, offsetX )
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Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation and alternative indexing semantics.
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
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var v = smeanlipw.ndarray( x.length, x, 1, 0 );
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// returns ~0.33333
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```
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The function has the following additional parameters:
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- **offsetX**: starting index for `x`.
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While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to calculate the [arithmetic mean][arithmetic-mean] for every other element in `x` starting from the second element
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var v = smeanlipw.ndarray( 4, x, 2, 1 );
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// returns 1.25
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- If `N <= 0`, both functions return `NaN`.
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- The underlying algorithm is a specialized case of Welford's algorithm. Similar to the method of assumed mean, the first strided array element is used as a trial mean. The trial mean is subtracted from subsequent data values, and the average deviations used to adjust the initial guess. Accordingly, the algorithm's accuracy is best when data is **unordered** (i.e., the data is **not** sorted in either ascending or descending order such that the first value is an "extreme" value).
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var smeanlipw = require( '@stdlib/stats/strided/smeanlipw' );
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var x = discreteUniform( 10, -50, 50, {
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'dtype': 'float32'
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});
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console.log( x );
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var v = smeanlipw( x.length, x, 1 );
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console.log( v );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/stats/strided/smeanlipw.h"
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```
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#### stdlib_strided_smeanlipw( N, \*X, strideX )
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Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.
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```c
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const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
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float v = stdlib_strided_smeanlipw( 4, x, 2 );
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// returns 4.0f
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```
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The function accepts the following arguments:
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- **N**: `[in] CBLAS_INT` number of indexed elements.
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- **X**: `[in] float*` input array.
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- **strideX**: `[in] CBLAS_INT` stride length for `X`.
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```c
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float stdlib_strided_smeanlipw( const CBLAS_INT N, const float *X, const CBLAS_INT strideX );
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```
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#### stdlib_strided_smeanlipw_ndarray( N, \*X, strideX, offsetX )
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Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation and alternative indexing semantics.
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```c
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const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
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float v = stdlib_strided_smeanlipw_ndarray( 4, x, 2, 0 );
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// returns 4.0f
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```
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The function accepts the following arguments:
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- **N**: `[in] CBLAS_INT` number of indexed elements.
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- **X**: `[in] float*` input array.
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- **strideX**: `[in] CBLAS_INT` stride length for `X`.
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- **offsetX**: `[in] CBLAS_INT` starting index for `X`.
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```c
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float stdlib_strided_smeanlipw_ndarray( const CBLAS_INT N, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/stats/strided/smeanlipw.h"
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#include <stdio.h>
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int main( void ) {
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// Create a strided array:
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const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
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// Specify the number of elements:
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const int N = 4;
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// Specify the stride length:
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const int strideX = 2;
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// Compute the arithmetic mean:
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float v = stdlib_strided_smeanlipw( N, x, strideX );
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// Print the result:
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printf( "mean: %f\n", v );
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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* * *
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<section class="references">
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## References
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- Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4 (3). Taylor & Francis: 419–20. doi:[10.1080/00401706.1962.10490022][@welford:1962a].
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- van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11 (3): 149–50. doi:[10.1145/362929.362961][@vanreeken:1968a].
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- Ling, Robert F. 1974. "Comparison of Several Algorithms for Computing Sample Means and Variances." _Journal of the American Statistical Association_ 69 (348). American Statistical Association, Taylor & Francis, Ltd.: 859–66. doi:[10.2307/2286154][@ling:1974a].
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- Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a].
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</section>
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<!-- /.references -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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* * *
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## See Also
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- <span class="package-name">[`@stdlib/stats/strided/dmeanlipw`][@stdlib/stats/strided/dmeanlipw]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a double-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.</span>
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- <span class="package-name">[`@stdlib/stats/strided/smean`][@stdlib/stats/strided/smean]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a single-precision floating-point strided array.</span>
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- <span class="package-name">[`@stdlib/stats/strided/smeanli`][@stdlib/stats/strided/smeanli]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a single-precision floating-point strided array using a one-pass trial mean algorithm.</span>
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
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[@stdlib/array/float32]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float32
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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[@welford:1962a]: https://doi.org/10.1080/00401706.1962.10490022
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[@vanreeken:1968a]: https://doi.org/10.1145/362929.362961
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[@ling:1974a]: https://doi.org/10.2307/2286154
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[@higham:1993a]: https://doi.org/10.1137/0914050
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<!-- <related-links> -->
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[@stdlib/stats/strided/dmeanlipw]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/strided/dmeanlipw
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[@stdlib/stats/strided/smean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/strided/smean
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[@stdlib/stats/strided/smeanli]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/strided/smeanli
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

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